This result can be read in a threefold way. At first, it is an existence
result for a supercritical Yamabe type problem in manifolds with boundary.
Secondly, it says that the family of solutions of this supercritical
problem is not a \(C^{2}\)  compact set, in fact it is not possible
find an uniform \(C^{2}\)  bound to the set \(\left\lbrace  u_{\varepsilon }\in H_{g}^{1}(M)\ :\ u_{\varepsilon }\text{ solution of (\ref {eq:Pmain})}\right\rbrace  _{\varepsilon }\) .
This represents an obstrucion to the extension of the compactness
result of [1]} to the supercritical case. Finally, Theorem REF 
has an interpretation in the sense of stabililty of Yamabe boundary
problem. Following Druet [2]}, we say that the Yamabe boundary
problem
\(\left\lbrace  \begin{array}{ll}L_{g}u=0 & \text{ on }M\\\frac{\partial }{\partial \nu }u+\frac{n-2}{2}h_{g}(x)u=(n-2)u^{\frac{n}{n-2}} & \text{ on }\partial M\end{array}\right.\) 
